THE DETERMINATION OF THE STRESS INTENSITY FACTORS OF A STEEL PLATE WITH DIFFERENT THICKNESS USING FEM
Keywords:
Stress Intensity Factor; Contact Pressure; Crack Growth; Finite Element Analysis; Fracture Mechanic
Abstract
This paper presents the finite element method for determining the stress intensity factors of steel plates
with different thickness having an elliptical cut-out in the center and subjected to different stresses. The
failure of the cracked parts affected by the stresses in the crack tip vicinity. The stress contribution can be
determined by the stress intensity factor K. For this purpose, an initial crack can be simulated and
modeled. Each of K corresponds to a crack propagation method. In this study the ANSYS software is used
for numerical modeling with several elements of solid type and nodes. a finer mesh is used around the
crack tip for more accurate results. Then an error percentage can be determined by using ANSYS results.
The present research is aimed to improve the formulation by including the effect of the crack-face closure
on the stress intensity factors K.
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References
ALBEDAH, A., BENYAHIA, F., DINAR, H. & BOUIADJRA, B.
B. 2013. Analytical formulation of the stress intensity
factor for crack emanating from central holes and
repaired with bonded composite patch in aircraft
structures. Composites Part B: Engineering, 45,
852-857.
BEREZHNITSKII, L. 1967. Propagation of cracks terminating
at the edge of a curvilinear hole in a plate. Soviet
materials science: a transl. of Fiziko-khimicheskaya
mekhanika materialov/Academy of Sciences of the Ukrainian SSR, 2, 16-23.
BROEK, D. 2012. Elementary engineering fracture
mechanics, Springer Science & Business Media.
CAMAS, D., GARCIA-MANRIQUE, J., ANTUNES, F. &
GONZALEZ-HERRERA, A. 2020. Three-dimensional
fatigue crack closure numerical modelling: crack
growth scheme. Theoretical and Applied Fracture
Mechanics, 102623.
CAMAS, D., GARCIA-MANRIQUE, J. &
GONZALEZ-HERRERA, A. 2011. Numerical study of
the thickness transition in bi-dimensional specimen
cracks. International Journal of Fatigue, 33, 921-928.
CHELL, G. & VITEK, V. 1979. Post yield solutions for fracture
mechanics analyses of cracks emanating from elliptic
holes. Engineering Fracture Mechanics, 11, 251-259.
CHEONG, S. & HONG, C. 1988. Analysis of cracks
emanating from a circular hole in an orthotropic plate
under mixed mode deformation. Engineering fracture
mechanics, 31, 237-248.
EVANS, R., CLARKE, A., HELLER, M. & STEWART, R. 2014.
Improved stress intensity factors for a single corner
crack at a loaded fastener hole. Engineering Fracture
Mechanics, 131, 570-586.
FELGER, J., STEIN, N. & BECKER, W. 2017. Asymptotic
finite fracture mechanics solution for crack onset at
elliptical holes in composite plates of finite-width.
Engineering Fracture Mechanics, 182, 621-634.
FOLIAS, E. & WANG, J.-J. 1990. On the three-dimensional
stress field around a circular hole in a plate of
arbitrary thickness. Computational Mechanics, 6,
379-391.
GARCIA-MANRIQUE, J., CAMAS, D., LOPEZ-CRESPO, P. &
GONZALEZ-HERRERA, A. 2013. Stress intensity
factor analysis of through thickness effects.
International Journal of Fatigue, 46, 58-66.
GUO, W. 1999. Three-dimensional analyses of plastic
constraint for through-thickness cracked bodies.
Engineering Fracture Mechanics, 62, 383-407.
GUO, W., ZHU, J. & GUO, W. 2020. Equivalent
thickness-based three dimensional stress fields and
fatigue growth of part-through cracks emanating from
a circular hole. Engineering Fracture Mechanics, 228,
106927.
HAJIMOHAMADI, M. & GHAJAR, R. 2019. Stress intensity
factors for cracks emanating from a circular hole in an
infinite quasi‐orthotropic plane. Fatigue & Fracture of
Engineering Materials & Structures, 42, 743-751.
HAN, Q., WANG, Y., YIN, Y. & WANG, D. 2015.
Determination of stress intensity factor for mode I
fatigue crack based on finite element analysis.
Engineering Fracture Mechanics, 138, 118-126.
HELLO, G., TAHAR, M. B. & ROELANDT, J.-M. 2012.
Analytical determination of coefficients in crack-tip
stress expansions for a finite crack in an infinite plane
medium. International Journal of Solids and
Structures, 49, 556-566.
ISIDA, M. 1966. Stress-intensity factors for the tension of an
eccentrically cracked strip.
JING, Z. & WU, X. 2015. Wide-range weight functions and
stress intensity factors for arbitrarily shaped crack
geometries using complex Taylor series expansion
method. Engineering Fracture Mechanics, 138,
215-232.
KHDIR, Y.-K., KANIT, T., ZAÏRI, F. & NAÏT-ABDELAZIZ, M.
2013. Computational homogenization of elastic–
plastic composites. International journal of solids and
structures, 50, 2829-2835.
KHDIR, Y.-K., KANIT, T., ZAÏRI, F. & NAÏT-ABDELAZIZ, M.
2014. Computational homogenization of plastic
porous media with two populations of voids. Materials
Science and Engineering: A, 597, 324-330.
KHDIR, Y.-K., KANIT, T., ZAÏRI, F. & NAÏT-ABDELAZIZ, M.
2015. A computational homogenization of random
porous media: Effect of void shape and void content
on the overall yield surface. European Journal of
Mechanics-A/Solids, 49, 137-145.
KHDIR, Y. K. 2019. Analytical and Numerical Investigation of
Hardening Behavior of Porous Media. Polytechnic
Journal, 9, 1-10.
LAM, K., TAY, T. & WANG, W. 1996. The Dugdale solution for
cracks at the edge of an elliptical hole in an infinite
and finite plate. Engineering fracture mechanics, 53,
97-106.
LEPORE, M., CARLONE, P., BERTO, F. & SONNE, M. R.
2017. A FEM based methodology to simulate multiple
crack propagation in friction stir welds. Engineering
Fracture Mechanics, 184, 154-167.
LI, B., KOYAMA, M., HAMADA, S. & NOGUCHI, H. 2019.
Effect analysis of stress-intensity-factor-range
decreasing rate for obtaining threshold
stress-intensity-factor-range. Theoretical and Applied
Fracture Mechanics, 104, 102377.
LIU, R., CHEN, T., LI, L. & TATEISHI, K. 2019. A practical
stress intensity factor formula for CFRP-repaired
steel plates with a central crack. Journal of
Constructional Steel Research, 162, 105755.
LIU, S. & DUAN, S. 2014a. Analytical solutions of cracks
emanating from an elliptic hole in an infinite plate
under tension. Chinese Journal of Mechanical
Engineering, 27, 1057-1063.
LIU, S. & DUAN, S. 2014b. Analytical solutions of cracks
emanating from an elliptical hole under shear.
Chinese Journal of Aeronautics, 27, 829-834.
MURAKAMI, Y. 1987. Stress intensity factors. NEWMAN, J. 1981. A crack-closure model for predicting
fatigue crack growth under aircraft spectrum loading.
Methods and models for predicting fatigue crack
growth under random loading. ASTM International.
NEWMAN JR, J. 1983. A nonlinear fracture mechanics
approach to the growth of small cracks. NATIONAL
AERONAUTICS AND SPACE ADMINISTRATION
HAMPTON VA LANGLEY RESEARCH CENTER.
NEWMAN JR, J. & DANIEWICZ, S. 2014. Predicting crack
growth in specimens with overloads and cold-worked
holes with residual stresses. Engineering Fracture
Mechanics, 127, 252-266.
NUI, L., CHEHIMI, C. & PLUVINAGE, G. 1994. Stress field
near a large blunted tip V-notch and application of the
concept of the critical notch stress intensity factor
(NSIF) to the fracture toughness of very brittle
materials. Engineering Fracture Mechanics, 49,
325-335.
PENG, D., WALLBRINK, C. & JONES, R. 2005. Stress
intensity factor solutions for finite body with
quarter-elliptical flaws emanating from a notch.
Engineering fracture mechanics, 72, 1329-1343.
PILKEY, W. D. & PILKEY, W. D. 1994. Formulas for stress,
strain, and structural matrices, Wiley New York.
ŞAHIN, H. & AYHAN, A. O. 2019. Three-Dimensional Mixed
Mode Stress Intensity Factors for Inclined Elliptical
Surface Cracks in Plates under Uniform Tensile Load.
Procedia Structural Integrity, 21, 38-45.
SCHIJVE, J. 2001. Fatigue of structures and materials,
Springer Science & Business Media.
SHARMA, D. S. & UKADGAONKER, V. G. Stress Intensity
Factors for Cracks Emanating from a Circular Hole in
Laminated Composite Infinite Plate Under Different
Loading Conditions. 2008 First International
Conference on Emerging Trends in Engineering and
Technology, 2008. IEEE, 781-786.
SHIVAKUMAR, V. & FORMAN, R. 1980. Green's function for
a crack emanating from a circular hole in an infinite
sheet. International Journal of Fracture, 16, 305-316.
SOUIYAH, M., ALSHOAIBI, A., MUCHTAR, A. & ARIFFIN, A.
2008. Stress intensity factor evaluation for crack
emanating from circular-hole using finite element
method. International review of mechanical
engineering, 2.
STAWIARSKI, A. 2018. The nondestructive evaluation of the
GFRP composite plate with an elliptical hole under
fatigue loading conditions. Mechanical Systems and
Signal Processing, 112, 31-43.
TADA, H., PARIS, P. & IRWIN, G. 2000. The analysis of
cracks handbook. New York: ASME Press, 2, 1.
VISHNUVARDHAN, S. 2020. Effect of constraints on stress
intensity factor for dissimilar metal plate with centre
crack under uniform tension. Materials Today
Communications, 22, 100807.
WEIßGRAEBER, P., FELGER, J., GEIPEL, D. & BECKER, W.
2016. Cracks at elliptical holes: stress intensity factor
and finite fracture mechanics solution. European
Journal of Mechanics-A/Solids, 55, 192-198.
WU, X., ZHAO, X., XU, W. & TONG, D. 2018. Discussions on
weight functions and stress intensity factors for radial
crack (s) emanating from a circular hole in an infinite
plate. Engineering Fracture Mechanics, 192,
192-204.
YAN, X. 2006. A numerical analysis of cracks emanating from
an elliptical hole in a 2-D elasticity plate. European
Journal of Mechanics-A/Solids, 25, 142-153.
YAN, X. 2007. Rectangular tensile sheet with single edge
crack or edge half-circular-hole crack. Engineering
Failure Analysis, 14, 1406-1410.
YANG, J., ZHOU, Y.-T., MA, H.-L., DING, S.-H. & LI, X. 2017.
The fracture behavior of two asymmetrical limited
permeable cracks emanating from an elliptical hole in
one-dimensional hexagonal quasicrystals with
piezoelectric effect. International Journal of Solids
and Structures, 108, 175-185.
B. 2013. Analytical formulation of the stress intensity
factor for crack emanating from central holes and
repaired with bonded composite patch in aircraft
structures. Composites Part B: Engineering, 45,
852-857.
BEREZHNITSKII, L. 1967. Propagation of cracks terminating
at the edge of a curvilinear hole in a plate. Soviet
materials science: a transl. of Fiziko-khimicheskaya
mekhanika materialov/Academy of Sciences of the Ukrainian SSR, 2, 16-23.
BROEK, D. 2012. Elementary engineering fracture
mechanics, Springer Science & Business Media.
CAMAS, D., GARCIA-MANRIQUE, J., ANTUNES, F. &
GONZALEZ-HERRERA, A. 2020. Three-dimensional
fatigue crack closure numerical modelling: crack
growth scheme. Theoretical and Applied Fracture
Mechanics, 102623.
CAMAS, D., GARCIA-MANRIQUE, J. &
GONZALEZ-HERRERA, A. 2011. Numerical study of
the thickness transition in bi-dimensional specimen
cracks. International Journal of Fatigue, 33, 921-928.
CHELL, G. & VITEK, V. 1979. Post yield solutions for fracture
mechanics analyses of cracks emanating from elliptic
holes. Engineering Fracture Mechanics, 11, 251-259.
CHEONG, S. & HONG, C. 1988. Analysis of cracks
emanating from a circular hole in an orthotropic plate
under mixed mode deformation. Engineering fracture
mechanics, 31, 237-248.
EVANS, R., CLARKE, A., HELLER, M. & STEWART, R. 2014.
Improved stress intensity factors for a single corner
crack at a loaded fastener hole. Engineering Fracture
Mechanics, 131, 570-586.
FELGER, J., STEIN, N. & BECKER, W. 2017. Asymptotic
finite fracture mechanics solution for crack onset at
elliptical holes in composite plates of finite-width.
Engineering Fracture Mechanics, 182, 621-634.
FOLIAS, E. & WANG, J.-J. 1990. On the three-dimensional
stress field around a circular hole in a plate of
arbitrary thickness. Computational Mechanics, 6,
379-391.
GARCIA-MANRIQUE, J., CAMAS, D., LOPEZ-CRESPO, P. &
GONZALEZ-HERRERA, A. 2013. Stress intensity
factor analysis of through thickness effects.
International Journal of Fatigue, 46, 58-66.
GUO, W. 1999. Three-dimensional analyses of plastic
constraint for through-thickness cracked bodies.
Engineering Fracture Mechanics, 62, 383-407.
GUO, W., ZHU, J. & GUO, W. 2020. Equivalent
thickness-based three dimensional stress fields and
fatigue growth of part-through cracks emanating from
a circular hole. Engineering Fracture Mechanics, 228,
106927.
HAJIMOHAMADI, M. & GHAJAR, R. 2019. Stress intensity
factors for cracks emanating from a circular hole in an
infinite quasi‐orthotropic plane. Fatigue & Fracture of
Engineering Materials & Structures, 42, 743-751.
HAN, Q., WANG, Y., YIN, Y. & WANG, D. 2015.
Determination of stress intensity factor for mode I
fatigue crack based on finite element analysis.
Engineering Fracture Mechanics, 138, 118-126.
HELLO, G., TAHAR, M. B. & ROELANDT, J.-M. 2012.
Analytical determination of coefficients in crack-tip
stress expansions for a finite crack in an infinite plane
medium. International Journal of Solids and
Structures, 49, 556-566.
ISIDA, M. 1966. Stress-intensity factors for the tension of an
eccentrically cracked strip.
JING, Z. & WU, X. 2015. Wide-range weight functions and
stress intensity factors for arbitrarily shaped crack
geometries using complex Taylor series expansion
method. Engineering Fracture Mechanics, 138,
215-232.
KHDIR, Y.-K., KANIT, T., ZAÏRI, F. & NAÏT-ABDELAZIZ, M.
2013. Computational homogenization of elastic–
plastic composites. International journal of solids and
structures, 50, 2829-2835.
KHDIR, Y.-K., KANIT, T., ZAÏRI, F. & NAÏT-ABDELAZIZ, M.
2014. Computational homogenization of plastic
porous media with two populations of voids. Materials
Science and Engineering: A, 597, 324-330.
KHDIR, Y.-K., KANIT, T., ZAÏRI, F. & NAÏT-ABDELAZIZ, M.
2015. A computational homogenization of random
porous media: Effect of void shape and void content
on the overall yield surface. European Journal of
Mechanics-A/Solids, 49, 137-145.
KHDIR, Y. K. 2019. Analytical and Numerical Investigation of
Hardening Behavior of Porous Media. Polytechnic
Journal, 9, 1-10.
LAM, K., TAY, T. & WANG, W. 1996. The Dugdale solution for
cracks at the edge of an elliptical hole in an infinite
and finite plate. Engineering fracture mechanics, 53,
97-106.
LEPORE, M., CARLONE, P., BERTO, F. & SONNE, M. R.
2017. A FEM based methodology to simulate multiple
crack propagation in friction stir welds. Engineering
Fracture Mechanics, 184, 154-167.
LI, B., KOYAMA, M., HAMADA, S. & NOGUCHI, H. 2019.
Effect analysis of stress-intensity-factor-range
decreasing rate for obtaining threshold
stress-intensity-factor-range. Theoretical and Applied
Fracture Mechanics, 104, 102377.
LIU, R., CHEN, T., LI, L. & TATEISHI, K. 2019. A practical
stress intensity factor formula for CFRP-repaired
steel plates with a central crack. Journal of
Constructional Steel Research, 162, 105755.
LIU, S. & DUAN, S. 2014a. Analytical solutions of cracks
emanating from an elliptic hole in an infinite plate
under tension. Chinese Journal of Mechanical
Engineering, 27, 1057-1063.
LIU, S. & DUAN, S. 2014b. Analytical solutions of cracks
emanating from an elliptical hole under shear.
Chinese Journal of Aeronautics, 27, 829-834.
MURAKAMI, Y. 1987. Stress intensity factors. NEWMAN, J. 1981. A crack-closure model for predicting
fatigue crack growth under aircraft spectrum loading.
Methods and models for predicting fatigue crack
growth under random loading. ASTM International.
NEWMAN JR, J. 1983. A nonlinear fracture mechanics
approach to the growth of small cracks. NATIONAL
AERONAUTICS AND SPACE ADMINISTRATION
HAMPTON VA LANGLEY RESEARCH CENTER.
NEWMAN JR, J. & DANIEWICZ, S. 2014. Predicting crack
growth in specimens with overloads and cold-worked
holes with residual stresses. Engineering Fracture
Mechanics, 127, 252-266.
NUI, L., CHEHIMI, C. & PLUVINAGE, G. 1994. Stress field
near a large blunted tip V-notch and application of the
concept of the critical notch stress intensity factor
(NSIF) to the fracture toughness of very brittle
materials. Engineering Fracture Mechanics, 49,
325-335.
PENG, D., WALLBRINK, C. & JONES, R. 2005. Stress
intensity factor solutions for finite body with
quarter-elliptical flaws emanating from a notch.
Engineering fracture mechanics, 72, 1329-1343.
PILKEY, W. D. & PILKEY, W. D. 1994. Formulas for stress,
strain, and structural matrices, Wiley New York.
ŞAHIN, H. & AYHAN, A. O. 2019. Three-Dimensional Mixed
Mode Stress Intensity Factors for Inclined Elliptical
Surface Cracks in Plates under Uniform Tensile Load.
Procedia Structural Integrity, 21, 38-45.
SCHIJVE, J. 2001. Fatigue of structures and materials,
Springer Science & Business Media.
SHARMA, D. S. & UKADGAONKER, V. G. Stress Intensity
Factors for Cracks Emanating from a Circular Hole in
Laminated Composite Infinite Plate Under Different
Loading Conditions. 2008 First International
Conference on Emerging Trends in Engineering and
Technology, 2008. IEEE, 781-786.
SHIVAKUMAR, V. & FORMAN, R. 1980. Green's function for
a crack emanating from a circular hole in an infinite
sheet. International Journal of Fracture, 16, 305-316.
SOUIYAH, M., ALSHOAIBI, A., MUCHTAR, A. & ARIFFIN, A.
2008. Stress intensity factor evaluation for crack
emanating from circular-hole using finite element
method. International review of mechanical
engineering, 2.
STAWIARSKI, A. 2018. The nondestructive evaluation of the
GFRP composite plate with an elliptical hole under
fatigue loading conditions. Mechanical Systems and
Signal Processing, 112, 31-43.
TADA, H., PARIS, P. & IRWIN, G. 2000. The analysis of
cracks handbook. New York: ASME Press, 2, 1.
VISHNUVARDHAN, S. 2020. Effect of constraints on stress
intensity factor for dissimilar metal plate with centre
crack under uniform tension. Materials Today
Communications, 22, 100807.
WEIßGRAEBER, P., FELGER, J., GEIPEL, D. & BECKER, W.
2016. Cracks at elliptical holes: stress intensity factor
and finite fracture mechanics solution. European
Journal of Mechanics-A/Solids, 55, 192-198.
WU, X., ZHAO, X., XU, W. & TONG, D. 2018. Discussions on
weight functions and stress intensity factors for radial
crack (s) emanating from a circular hole in an infinite
plate. Engineering Fracture Mechanics, 192,
192-204.
YAN, X. 2006. A numerical analysis of cracks emanating from
an elliptical hole in a 2-D elasticity plate. European
Journal of Mechanics-A/Solids, 25, 142-153.
YAN, X. 2007. Rectangular tensile sheet with single edge
crack or edge half-circular-hole crack. Engineering
Failure Analysis, 14, 1406-1410.
YANG, J., ZHOU, Y.-T., MA, H.-L., DING, S.-H. & LI, X. 2017.
The fracture behavior of two asymmetrical limited
permeable cracks emanating from an elliptical hole in
one-dimensional hexagonal quasicrystals with
piezoelectric effect. International Journal of Solids
and Structures, 108, 175-185.
Published
2021-01-07
How to Cite
KHDIR, Y. K. (2021). THE DETERMINATION OF THE STRESS INTENSITY FACTORS OF A STEEL PLATE WITH DIFFERENT THICKNESS USING FEM. Journal of Duhok University, 23(2), 679-692. https://doi.org/10.26682/csjuod.2020.23.2.53
Section
Pure and Engineering Sciences
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